Lei, Pei Dong et al., L p and L . norm estimates of the cost of the controllability for heat equations, Acta mathematica Sinica. English series (Print) , 25(8), 2009, pp. 1305-1324
This paper is concerned with the bound of the cost of approximate controllability and null controllability of heat equations, i.e., the minimal L p norm and L . norm of a control needed to control the system approximately or a control needed to steer the state of the system to zero. The methods we use combine observability inequalities, energy estimates for heat equations and the dual theory.